SOLUTION: I need to design a fair race for two animals. The animals need to finish in the same amount of time. I can give the slower animal a shorter distance. The race can be any length.

Question 1109300: I need to design a fair race for two animals. The animals need to finish in the same amount of time. I can give the slower animal a shorter distance. The race can be any length.
I need to develop a system of two linear equations showing the distance each animal can travel to model a fair race. I need to define all variables. I then need to graph the system to prove they have an equal chance of winning and explain how the graph proves the race is fair.
I chose an elephant at 25 mph and a lion at 50 mph.
I know I need to use Y = mx + b
I am just really confused on what to put where in order to get the answer and how to graph the results. I can see that the elephant needs twice the amount of time as the lion. In order to go 200 miles, the lion would take 4 hours and the elephant 8 hours. The elephant would need to start 4 hours ahead of the lion in order to finish at the same time.
What are the steps I need to take to show that on paper? I am so confused.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I would make it a shorter race, because I do not think a lion can run at 50 mph for 4 hours.
I imagine a straight race track, maybe 5 miles.
= time in hours from the start of the race.
= the position of each animal (in miles from the 0 mile marker).
The lion starts at the 0 mile marker,
so its position will be given by for .
The elephant will start the race at the 0.5 mile marker,
so its position will be given by for .

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